Average Error: 0.1 → 0.1
Time: 4.3s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)
double f(double x) {
        double r107544 = 1.0;
        double r107545 = x;
        double r107546 = 0.253;
        double r107547 = 0.12;
        double r107548 = r107545 * r107547;
        double r107549 = r107546 + r107548;
        double r107550 = r107545 * r107549;
        double r107551 = r107544 - r107550;
        return r107551;
}
↓
double f(double x) {
        double r107552 = x;
        double r107553 = -r107552;
        double r107554 = 0.12;
        double r107555 = 0.253;
        double r107556 = fma(r107554, r107552, r107555);
        double r107557 = 1.0;
        double r107558 = fma(r107553, r107556, r107557);
        return r107558;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))